Information on Result #691588
Linear OA(1621, 1048581, F16, 5) (dual of [1048581, 1048560, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- linear OA(1621, 1048576, F16, 5) (dual of [1048576, 1048555, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1616, 1048576, F16, 4) (dual of [1048576, 1048560, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OA(828, 1048581, S8, 5) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1621, 1048581, F16, 2, 5) (dual of [(1048581, 2), 2097141, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (16, 21, 1048581)-net over F16 | [i] | ||
| 4 | Linear OOA(1621, 524290, F16, 2, 5) (dual of [(524290, 2), 1048559, 6]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1621, 524290, F16, 5, 5) (dual of [(524290, 5), 2621429, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |